Electrical filters have long been used in the processing of electrical signals. In particular, such electrical filters are used to select desired electrical signal frequencies from an input signal by passing the desired signal frequencies, while blocking or attenuating other undesirable electrical signal frequencies. Filters may be classified in some general categories that include low-pass filters, high-pass filters, band-pass filters, and band-reject filters, indicative of the type of frequencies that are selectively passed by the filter. Further, filters can be classified by type, such as Butterworth, Chebyshev, Inverse Chebyshev, and Elliptic, indicative of the type of bandshape frequency response (frequency cutoff characteristics) the filter provides relative to the ideal frequency response.
Microwave filters are generally built using two circuit building blocks: a plurality of resonators, which store energy very efficiently at one frequency, f0; and couplings, which couple electromagnetic energy between the resonators to form multiple stages or poles. For example, a four-pole filter may include four resonators. The strength of a given coupling is determined by its reactance (i.e., inductance and/or capacitance). The relative strengths of the couplings determine the filter shape, and the topology of the couplings determines whether the filter performs a band-pass or a band-reject function. The resonant frequency f0 is largely determined by the inductance and capacitance of the respective resonator. For conventional filter designs, the frequency at which the filter is active is determined by the resonant frequencies of the resonators that make up the filter. Each resonator must have very low internal resistance to enable the response of the filter to be sharp and highly selective for the reasons discussed above. This requirement for low resistance tends to drive the size and cost of the resonators for a given technology.
The type of filter used often depends upon the intended use. In communications applications, band-pass filters are conventionally used in cellular base stations and other telecommunications equipment to filter out or block RF signals in all but one or more predefined bands. For example, such filters are typically used in a receiver front-end to filter out noise and other unwanted signals that would harm components of the receiver in the base station or telecommunications equipment. Placing a sharply defined band-pass filter directly at the receiver antenna input will often eliminate various adverse effects resulting from strong interfering signals at frequencies near the desired signal frequency. Because of the location of the filter at the receiver antenna input, the insertion loss must be very low so as to not degrade the noise figure. In most filter technologies, achieving a low insertion loss requires a corresponding compromise in filter steepness or selectivity.
In commercial telecommunications applications, it is often desirable to filter out the smallest possible passband using narrow-band filters to enable a fixed frequency spectrum to be divided into the largest possible number of frequency bands, thereby increasing the actual number of users capable of being fit in the fixed spectrum. Of most particular importance is the frequency ranges of 800-900 MHz range for analog cellular communications, and 1,800-2,200 MHz range for personal communication services (PCS). With the dramatic rise in wireless communications, such filtering should provide high degrees of both selectivity (the ability to distinguish between signals separated by small frequency differences) and sensitivity (the ability to receive weak signals) in an increasingly hostile frequency spectrum.
Historically, filters have been fabricated using normal; that is, non-superconducting conductors. These conductors have inherent lossiness, and as a result, the circuits formed from them have varying degrees of loss. For resonant circuits, the loss is particularly critical. The quality factor (Q) of a device is a measure of its power dissipation or lossiness. For example, a resonator with a higher Q has less loss. Resonant circuits fabricated from normal metals in a microstrip or stripline configuration typically have Q's at best on the order of four hundred. With the discovery of high temperature superconductivity in 1986, attempts have been made to fabricate electrical devices from high temperature superconductor (HTS) materials. The microwave properties of HTSs have improved substantially since their discovery. Epitaxial superconductor thin films are now routinely formed and commercially available.
Currently, there are numerous applications where microstrip narrow-band filters that are as small as possible are desired. This is particularly true for wireless applications where HTS technology is being used in order to obtain filters of small size with very high resonator Q's. The filters required are often quite complex with perhaps twelve or more resonators along with some cross couplings. Yet the available size of usable substrates is generally limited. For example, the wafers available for HTS filters usually have a maximum size of only two or three inches. Hence, means for achieving filters as small as possible, while preserving high-quality performance are very desirable. In the case of narrow-band microstrip filters (e.g., bandwidths of the order of 2 percent, but more especially 1 percent or less), this size problem can become quite severe.
In addition to size and loss considerations, of particular interest to the present inventions is the minimization of intermodulation distortion (IMD), which has become increasingly important in microwave and RF amplifier design. IMD is an undesirable phenomenon that occurs when two or more signals of different frequencies are present at the input of a non-linear device, thereby generating spurious emissions at frequencies different from the desired harmonic frequencies of the filter. The frequencies of the intermodulation products are mathematically related to the frequencies of the original input signals, and can be computed by the equation: mf1±nf2, where f1 is the frequency of the first signal, f2 is the frequency of the second signal, and m, n=0, 1, 2, 3, . . . . Intermodulation products are generated at various orders, with the order of a distortion product given by the sum of m+n.
As illustrated in FIG. 1, the second order intermodulation products of two fundamental signals at f1 and f2 will occur at f1+f2, f2−f1, 2f1, and 2f2, and the third order intermodulation products of the two signals at f1 and f2 will occur at 2f1+f2, 2f1−f2, f1+2f2, f1−2f2 (or 2f1±f2 and 2f2±f1), 3f1, and 3f2, where 2f1 is the second harmonic of f1, 2f2 is the second harmonic of f2, 3f1 is the third harmonic of f1, and 3f2 is the third harmonic of f2. While bandpass filtering may be an effective means of eliminating most of the undesired intermodulation products without affecting the inband performance, the third order intermodulation products 2f1−f2, 2f2−f1 are usually too close to the fundamental signals f1, f2 to be filtered out, as shown in FIG. 1. If the intermodulation products are within the passband, filtering becomes impossible.
As a practical example, when strong signals from more than one transmitter are present at the input of a receiver, as is commonly the case in telephone systems, IMD products will be generated. The level of these undesired IMD products is a function of the power received and the linearity of the receiver/preamplifier. As a general rule, the second order intermodulation products will increase at a rate of the input signal squared, and the third order intermodulation products will increase at a rate of the input signal cubed. Thus, second order intermodulation products have an amplitude proportional to the square of the input signal, whereas the third order intermodulation products have an amplitude proportional to the cube of the input signal.
Thus, if two input signals, equal in magnitude, each rise by 1 dB, then the second order intermodulation products will rise by 2 dB, and the third order intermodulation products will rise by 3 dB. Thus, although the levels of third order intermodulation products are initially very small compared to lower order intermodulation products (which generally dominate), the third order intermodulation products grow at higher rates. Therefore, when attempting to increase the power-handling of a non-linear device, such as an amplifier, the third order intermodulation products, which are closest to the passband of interest (i.e., 2f1−f2, 2f2−f1) are the greatest concern.
The exponential effect of the intermodulation products will hold true as long as the device is in the linear region. As shown in FIG. 2, the device goes into compression at a point where the output of the device becomes non-linear with respect to its input. If the output levels of the fundamental signal, second order intermodulation products, and third order intermodulation products are plotted against an input level, there would theoretically be points where the levels of the second and third order intermodulation products intercept the fundamental signal. These points are known respectively as a second order intercept point (SOI) and a third order intercept point (TOI; also known as IP3). It is important note that in practice, this is an unrealistic condition, since the device will saturate long before the intercept point is reached. The input power level at which the intercept points occur is referred to as an IP value. If the exponent of the power dependence of the IMD product is n, the IP value is denoted by IPn. For example, for second order IMD products, the IP value is IP2, and for third order IMD products, the IP value is IP3. The concept of an IMD intercept point has been developed to help quantify a device's IMD performance, with the IMD performance improving as the IP value is higher.
While only small losses occur in many superconducting filters, such filters are inherently nonlinear, which can limit the IP value of, for example, a base-station receiver to values that are too small for certain demanding applications. For example, sometimes conventional superconducting filters cannot be effectively used in wireless telecommunication networks where the base stations are co-located with strong specialized mobile radio (SMR) transmitters for with other cellular/PCS service providers, because the power levels of out-of-band signals from these other systems can be too high and result in IMD that reduces the receiver sensitivity. As a result, the superconducting filters are unable to adequately filter out the undesired out-of-band signals.
The performance of the filter also changes with manufacturing process variations of the resonators and filters. Although some filters might be manufactured to achieve the required filtering capabilities for filtering out competing system out-of-band signaling, many of them would fail in such applications, and are thus sorted out during testing, resulting in low filter manufacturing yields. With respect to HTS technology, the non-linearities of an RF filter, and thus the IMD exhibited by the filter, may be minimized by increasing the size of the filter. However, as discussed above, it is desirable that the size of an HTS filter be minimized as much as possible. There, thus, remains a need to minimize the IMD (thus, maximizing the IP value) of a filter without substantially increasing its size.